#vector with the squares of 1:10

x <- numeric(10) #vector de 0

for (i in 10:1) {
  x[i] <- i^2
}
x

sapply(1:10, function(x) x^2)
(1:10)^2

A <- rbind(1:2,3:4)
apply(A,2, function(x) var(x)) #by columns
apply(A,1, function(x) var(x)) #by rows


# EX 11 -------------------------------------------------------------------
#a)
#3 formas de hacerlo
f1 <-  function(n) sum((1:n)^2)

f2 <-  function(n) sum(sapply(1:n, function(x) x^2))

f3 <-  function(n){
  x <- 0
  for (i in 1:n) {
    x <- c(x,i^2)
  }
return(sum(x))
}

f1(10)
f2(10)
f3(10)
#b)

f <- function(N) plot(n <- c(1:N), sum((1:n)^(1/2)))